Modelling of viscoelastic materials and creep behaviour

Abstract

The paper is mainly motivated by the observation that, in creep tests, a secondary stage occurs where the strain rate is relatively small and roughly constant. The paper first examines the well-known models based on connections of springs and dashpots (Maxwell, Kelvin–Voigt, standard linear solid, Wiechert) and finds that they are far from showing the constant strain rate of the secondary stage. Next a simple model is considered where a Maxwell element is connected in parallel with a dashpot. The resulting stress–strain relation is established and the secondary stage is investigated thus showing that the nearly constant strain rate occurs. Moreover, the stress–strain relation is shown to be compatibile with the second law of thermodynamics the stress being the sum of two terms. One of them is purely dissipative and the other emerges from a Graffi–Volterra free energy potential.